Generalized marcum q-function
In statistics, the generalized Marcum Q-function of order $${\displaystyle \nu }$$ is defined as $${\displaystyle Q_{\nu }(a,b)={\frac {1}{a^{\nu -1}}}\int _{b}^{\infty }x^{\nu }\exp \left(-{\frac {x^{2}+a^{2}}{2}}\right)I_{\nu -1}(ax)\,dx}$$where $${\displaystyle b\geq 0}$$ and See more Finite integral representation The generalized Marcum Q-function can alternatively be defined as a finite integral as However, it is … See more It is convenient to re-express the Marcum Q-function as $${\displaystyle P_{N}(X,Y)=Q_{N}({\sqrt {2NX}},{\sqrt {2Y}}).}$$ See more 1. ^ J.I. Marcum (1960). A statistical theory of target detection by pulsed radar: mathematical appendix, IRE Trans. Inform. Theory, vol. … See more Based on monotonicity and log-concavity Various upper and lower bounds of generalized Marcum-Q function can be obtained using monotonicity and log-concavity of the function $${\displaystyle \nu \mapsto Q_{\nu }(a,b)}$$ and the fact that we have … See more The generalized Marcum Q-function can be used to represent the cumulative distribution function (cdf) of many random variables: • If See more WebNov 5, 2004 · Summary As alluded to in Chapter 4, the alternative representations of the Gaussian and Marcum Q-functions in the desired form are the key mathematical tools in unifying evaluation of the average e...
Generalized marcum q-function
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WebJun 13, 2016 · Closed-form solutions for the general integrals in terms of Meijer's G-function are derived and validated by comparing with the analytic expressions for the existing integrals involving the generalized Marcum Q-function, which are the special cases of the general integrals addressed in this letter. WebMay 17, 2024 · Noncentral chi-squared Distribution. ¶. The distribution of ∑ i = 1 ν ( Z i + δ i) 2 where Z i are independent standard normal variables and δ i are constants. λ = ∑ i = 1 …
WebNov 1, 2010 · In this paper we consider the generalized Marcum Q-function of order ν > 0 real, defined by Q ν (a, b) = 1 a ν-1 ∫ b ∞ t ν e-t 2 + a 2 2 I ν-1 (at) dt, where a > 0, b ⩾ 0 …
WebAug 1, 2009 · The study of the generalized Marcum function of the second kind is motivated by the importance of the generalized Marcum Q-function in the electrical engineering literature, which was... WebSep 1, 2008 · The generalized Marcum Q-function, Qm(a,b), is here explained geometrically as the probability of a 2m-dimensional, real, Gaussian random vector, whose mean vector has a Frobenius norm of a, lying … Expand. 37. View 2 excerpts; Save. Alert. Supplements to Known Inequalities for Some Special Functions.
WebOct 16, 2010 · the generalized marcum q − function: an orthogonal pol ynomial approach 3 where x, z ∈ R and α > − 1 . Now, changing in (4) z with − z and taking into …
WebThe generalized Marcum Q -function of order m is defined by. Q m ( a, b) = 1 a m − 1 ∫ b ∞ x m exp ( − x 2 + a 2 2) I m − 1 ( a x) d x, where Im – 1 is the modified Bessel function … costruzione veneziaWebMay 1, 2015 · A novel power series representation of the generalized Marcum $Q-$function of positive order involving generalized Laguerre polynomials is presented. The absolute convergence of the proposed... costruzione verba timendi latinoWebQ = marcumq(a,b) computes the Marcum Q-function of order 1 for noncentrality parameter a and argument b. Use this syntax to calculate the special case of the generalized … costruzione verbo likeWebWe then apply the derived results to assess the secrecy performance of the system in terms of the average signal-to-noise ratio (SNR) as a function of the $\kappa$ and $\mu$ fading parameters. We observed that for fixed values of the eavesdropper's average SNR, increases in the average SNR of the main channel produce a higher probability of ... macs matematica absolutamentehttp://webhome.auburn.edu/~yzs0078/paper/journal/MarcumQ_ineq_AMC08.pdf costruzione vanWebThe generalized Marcum $ Q-$ function: an orthogonal polynomial approach. Szilárd András. 2010, Arxiv preprint arXiv:1010.3348. Continue Reading. Download Free PDF. Download. Related Papers. Performance Study of Nakagami-m Fading Channels with Correlated Unbalanced Branches. Hakim Alhussien. macsi treatment applicationWebApr 10, 2024 · First, we derive the analytical expression of the outage probability with a generalized Marcum Q-function. Then, we develop an alternating optimization algorithm to minimize the outage probability by capitalizing on the generalized eigenvalue-eigenvectors. ma csl registration